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In today’s competitive and dynamic market conditions, the effective collaboration of partners and coordination of all strategic, tactical, and operational activities and decisions within the supply chain is prerequisite (Shen, 2005). Recently, lots of integrated models have been studied within the supply chain networks approach. The integrated models in supply chain networks include inventory-routing problems, location-inventory problems, and production-inventory models (Tarantilis, 2008). This paper mostly deals with location-inventory problems integrated with production rates’ decision for manufacturers.
The previous related works on integrated models can be viewed and classified based on the level of integration, complexities, decision variables, modeling techniques, and solution algorithm. In what follows, these related works are briefly discussed.
The first classification is the level of integration which include location-inventory, inventory-routing, and production-inventory. There are many researchers who developed models for location-inventory problems. Erlebacher and Meller (2000) develop a non-linear model for distribution centers’ locations accompanied with inventory holding costs at DCs (Distribution centers) in which the location of DCs were assumed discrete variables. Teo, Ou, and Goh (2001) propose a location-inventory model which considered centralization of DCs and did not include transportation costs. The models in this category are further developed by other researchers to include more decision variables and factors. In one study, Daskin, Coullard, and Shen (2001) develop an integrated approach to determine the location, number of the DCs and the amount of safety stock hold at each DC. They develop a nonlinear integer program solved by a Lagrangian Relaxation solution algorithm. The outputs of their approach are number of DCs to be established along with the level of inventory to be kept at each DC. In another study, Miranda and Garido (2004) work on a nonlinear three-level location-inventory model with capacitated DCs. The manufacturers are pre-determined with no inventory hold at them. They developed a mixed integer nonlinear programing, and a Lagrangian-based heuristic and sub-gradient method were developed in order to solve that. Miranda and Garido (2006) develop a hierarchical two-phase heuristic in order to optimize the service level in a three level distribution network design. In the first phase, the service level is optimized and in the second level, location-inventory decision is considered. These two steps are iterated until equilibrium is reached with regard to service level. Berman, Krass, and Tajbakhsh (2012) consider a location-inventory model where DCs follow a periodic review inventory policy. The aim is to determine inventory policy parameters at the DCs together with location- allocation decisions. A Lagrangian relaxation algorithm is proposed to solve the model. In a problem that can be considered as location-inventory, Askin, Baffo, and Xia (2014) develop a model for logistics network and warehouse location with inventory consideration. The model solved by a genetic algorithm which is problem specific.